Abstract
In this paper one investigates overdetermined elliptic systems with constant coefficients for which one can pose general boundary-value problems without overdetermination in the boundary conditions. One finds the algebraic condition which characterizes the indicated class of systems. It is shown that the general boundary-value problems for such systems are Noetherian in the subspace of vector-functions satisfying some purely differential consistency conditions.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. nA. Steklova AN SSSR, Vol. 47, pp. 138–154, 1974.
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Solonnikov, V.A. A class of Noetherian overdetermined elliptic boundary-value problems. J Math Sci 9, 244–259 (1978). https://doi.org/10.1007/BF01578547
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DOI: https://doi.org/10.1007/BF01578547